#5. looks fine.
The roots are { +√(6) , -√(6) , -2, 2 }
#6. 12x³ + 26x² - 10x
factor out 2x
2x(6x² + 13x - 5) = 0
one root is zero
factor for other two roots, only 5×1 = 5
(3x-1)(2x+5)
3x - 1 = 0
3x = 1
x = 1/3
2x + 5 = 0
2x = -5
x = -5/2
roots are { 0, 1/3, -5/2 }
EDIT** forgot #7
#7. 125x³ + 8 = 0
125x³ = -8
x³ = -8/125
x = ∛(-8/125)
root of a fraction is the root of the numerator and denominator, negative can be on either numerator or denominator. overall fraction should be negative to subtract from the 8 to give zero.
∛(-8) = +/- 2
∛(125) = 5
root { -2/5 }
